Wei Shi Lim

Producer-Supplier Contracts with Incomplete Information

This paper investigates the contract design problem of a producer when he purchases parts from a supplier, and there is incomplete information regarding the quality of the parts. This is the first game-theoretic model of quality control that captures this informational asymmetry. We focus on two compensation schemes embedded in the contract, namely, price rebate when inspection is done upon receipt of the parts and warranty. We show that when a full-price rebate is not possible and the producer and the supplier have to share the damage costs, an optimal contract is such that the supplier compensates the producer by the same amount, regardless of his quality type. However, a supplier with low quality is more likely to be offered a contract with an inspection scheme, while a supplier with high quality is constrained with a warranty scheme. We also show that when the producer need not share the cost in exactly one of the compensation schemes, he may still offer the other compensation scheme to a supplier type depending on the relative costs involved, the maximum compensation cost acceptable by all supplier types, and his ex ante beliefs about the quality level of the supplier.

A lemons market? An incentive scheme to induce truth-telling in third party logistics providers

Abstract In this paper, we develop a game-theoretic model that studies the contract design problem of a third party logistics buyer when he is faced with a third party logistics provider and the quality of service and the cost of providing the service are private information to the latter. We apply the Revelation Principle to our analysis and characterise the optimal contract. We show that the contract offered to the service provider with low capability does not include any penalty for failure to comply to preset standards; neither does it include a gain-sharing scheme – the remuneration consists of an initial fixed payment which is independent of the level of performance. However, the contract offered to the service provider with high capability includes either a penalty scheme or a gain-sharing scheme. Furthermore, the more attractive the gain-sharing scheme (or alternatively, the more severe the penalty), the less the initial remuneration and vice versa. Finally, we prove that the proposed optimal contract is independent of the ex-ante beliefs which the service buyer has on the capability and the cost of the service provider.

Optimal product rollover strategies

As product life cycles shortened, many firms introduce new products and phase out old products frequently. To plan for a successful product rollover; i.e., introduce a new product and eliminate an old product successfully, a firm needs to determine the prices of both products as well as the time to launch the new product and the time to phase out the old product. In this paper, we develop an analytical model to analyze the profits associated with two product rollover strategies: single-product rollover and dual-product rollover. The single-product rollover strategy calls for simultaneous introduction of the new product and elimination of the old product. For the dual-product rollover, we introduce the new product first and then phase out the old product eventually. We determine the optimal prices of both products as well as the optimal time to execute these product rollover strategies. Moreover, we determine the conditions under which the dual-product rollover strategy is optimal.

Rendezvous Search on the Line with More Than Two Players

Suppose n blind, speed one, players are placed by a random permutation onto the integers 1 to n , and each is pointed randomly to the right or left. What is the least expected time required form m ≤ n of them to meet together at a single point? If they must all use the same strategy we call this time the symmetric rendezvous value R n , m s ; otherwise the asymmetric value R n , m a . We show that R 3,2 a = 47/48, and that R n , n s is asymptotic to n /2. These results respectively extend those for two players given by Alpern and Gal (Alpern, S., S. Gal. 1995. Rendezvous search on the line with distinguishable players. SIAM J. Control Optim. 33 1270–1276.) and Anderson and Essegaier (Anderson, E. J., S. Essegaier. 1995. Rendezvous search on the line with indistinguishable players. SIAM J. Control Optim. 33 1637–1642.).

An auction model arising from an Internet search service provider

Abstract Most search service providers such as Lycos and Google either produce irrelevant search results or unstructured company listings to the consumers. To overcome these two shortcomings, search service providers such as GoTo.com have developed mechanisms for firms to advertise their services and for consumers to search for the right services. To provide relevant search results, each firm who wishes to advertise at the GoTo site must specify a set of keywords. To develop structured company listings, each firm bids for priority listing in the search results that appear on the GoTo site. Since the search results appear in descending order of bid price, each firm has some control over the order in which the firm appears on the list resulting from the search. In this paper, we present a one-stage game for two firms that captures the advertising mechanism of a search service provider (such as GoTo). This model enables us to examine the firm’s optimal bidding strategy and evaluate the impact of various parameters on the firm’s strategy. Moreover, we analyze the conditions under which all firms would increase their bids at the equilibrium. These conditions could be helpful to the service provider when developing mechanisms to entice firms to submit higher bids.

A rendezvous-evasion game on discrete locations with joint randomization

We consider a problem proposed by S. Alpern ( European Journal of Operational Research (1997)) of how two players can optimally rendezvous while at the same time evading an enemy searcher. This problem can be modelled as a two-person, zero-sum game between the rendezvous team R (with agents R 1 , R 2 ) and the searcher S. This paper gives the first solution to such a rendezvous-evasion game by considering a version that is discrete in time and space, as in the pure rendezvous problem of Anderson and Weber ( Journal of Applied Probability 28 , pp. 839–851). R 1 , R 2 and S start at different locations among the n identical locations where there is no common labelling and at each integer time they may rellocate to any one of the n locations. When some location is occupied by more than one player, the game ends. If S is at this location, S (maximizer) wins and the payoff is 1; otherwise R (minimizer) wins and the payoff is 0. The value of the game is the probability that S wins under optimal play. We assume that R 1 and R 2 can jointly randomize their strategies. When n equals 3, the value of the game is . We also prove that the value of the game is bounded above by asymptotically. If, in addition, the players share a common notion of a directed cycle containing all the n locations (while still able to move between any two locations), the value of the game is ((1 – 2/ n ) n– 1 + l)/2. Finally, we prove that with this extra information, R can secure a strictly lower value for all n .

Entry of Copycats of Luxury Brands

We develop a game-theoretic model to examine the entry of copycats and its implications by incorporating two salient features; these features are two product attributes, i.e., physical resemblance and product quality, and two consumer utilities, i.e., consumption utility and status utility. Our equilibrium analysis suggests that copycats with a high physical resemblance but low product quality are more likely to successfully enter the market by defying the deterrence of the incumbent. Furthermore, we show that higher quality can prevent the copycat from successfully entering the market. Finally, we show that the entry of copycats does not always improve consumer surplus and social welfare. In particular, when the quality of the copycat is sufficiently low, the loss in status utility from consumers of the incumbent product overshadows the small gain in consumption utility from buyers of the copycat, leading to an overall decrease in consumer surplus and social welfare.

Market structure and the value of overselling under stochastic demands

In the operations management literature, traditional revenue management focused on pricing and capacity allocation strategies in a two-period model with stochastic demand. Inspired by travel and lodging industries, we examine a two-period model in which each seller may also adopt the overselling strategy to customers whose valuations are differentiated by timing of arrivals. Widely seen as a popular hedge against consumers’ skipping reservations, we extend the stylized approaches of Biyalogorsky, Carmon, Fruchter, and Gerstner (1999) and Lim (2009) to understand the value of overselling under various market structures. We find that contrary to existing literature, the impact of period-two pricing competition from overselling spills over to period-one such that overselling may not always be a (weakly) dominant strategy once unlimited early demand ceases to hold in a duopoly regime. We provide some numerical studies on the existence of multiple equilibria at the capacity allocation level which actually lead to different selling strategies at the equilibrium despite identical market conditions and firm characteristics.

The Impact of the Potential Entry of Copycats: Entry Conditions, Consumer Welfare, and Social Welfare

This article examines the implications of the potential entry of a copycat who produces and sells a copycat (i.e., imitation) product that competes with the incumbent product. By analyzing a two-period dynamic noncooperative game between these two firms, we identify conditions under which the copycat can gain successful market entry. More importantly, we find that the potential entry of a copycat creates (implicit) pressure for the incumbent to lower its selling price; hence, it improves consumer welfare. Finally, we identify conditions under which the potential entry of a copycat can increase social welfare (i.e., consumer welfare and the profit of both firms).